Josephson interferometry and Shapiro step measurements of superconductor-ferromagnet-superconductor $0\text{−}\pi$ junctions

We report the observation of the $0\text{−}\pi$ junction state in superconductor-ferromagnet-superconductor Josephson junctions arising from variations in the effective barrier thickness $d∕{\xi }_F$. By varying the temperature, the junctions can be tuned from the 0- to the $\pi$-state through an intermediate regime in which parts of the junction are in each state. A signature of the $0\text{−}\pi$ regime is that the usual peak in the critical current diffraction pattern at zero magnetic field becomes a dip, evidence for sign changes in the critical current density. In some junctions, the zero-field critical current does not vanish at any temperature and half-integer Shapiro steps are observed, indicating the presence of spontaneous supercurrents circulating within the junctions around the $0\text{−}\pi$ interfaces.

Figure 1

(a) Stepped ferromagnetic barrier deduced from critical current vs applied magnetic flux measurements. (b) Diffraction patterns at a series of temperatures showing deviations from Fraunhofer behavior at low temperatures. (c) Simulated diffraction patterns using the deduced ferromagnetic barrier profile.

Figure 2

(a) Calculated temperature variation of the critical current for junction sections 1 and 2 and for the entire junction. The thin region remains in the 0 state at all temperatures while the thick region crosses from the 0 state into the $\pi$ state. (b) Measured critical current vs temperature at zero applied magnetic field dips but remains finite.

Figure 3

(a) Current-voltage characteristics showing rf-induced Shapiro steps both at the usual voltages $nh{f}_{rf}∕2e$ and at half-integer values $nh{f}_{rf}∕4e$. (b) Temperature dependence of the maximum (power-optimized) critical current steps, showing that the integer steps scale with the junction critical current whereas the half-integer steps occur only at temperatures near the minimum in the critical current.

Figure 4

Phase diagram mapping the region of $w_0∕{\lambda }_{J0}$ and $w_{\pi }∕{\lambda }_{J\pi }$ values for which a spontaneous circulating current flows around the $0\text{−}\pi$ step edge. In the shaded region, the phase drop across the junction $\varphi$ and current density $J$ vary spatially along the junction width. Outside this region, the phase is uniform with value 0 or $\pi$ and no spontaneous currents flow in the junction.